Using Theorem 6.1, prove that a line drawn through the mid-point of one side of a triangle parallel to another side bisects the third side.
Triangles
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Question

Using Theorem 6.1, prove that a line drawn through the mid-point of one side of a triangle parallel to another side bisects the third side.

KnowledgeBoat · Accepted Answer

Let ABC be the triangle and D be the mid-point of AB and DE || BC. By theorem 6.1, If a line is drawn parallel to one side of a triangle to intersect the other two sides at distinct points, the other two sides are divided in the same ratio. So, In △ ABC, Since, AE = EC. ∴ E bisects AC. Hence, proved that a line drawn through the mid-point of one side of a triangle parallel to another side bisects the third side.

Mathematics

Using Theorem 6.1, prove that a line drawn through the mid-point of one side of a triangle parallel to another side bisects the third side.

Triangles

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